TABLE 7.

Summary of sleep-related criticality literature.

Study	Study population	Modality	Analysis	Main findings
Nikulin and Brismar, 2004	12 healthy adults	EEG with eyes-open and eyes-closed	DFA	• LRTC in alpha oscillations were not changed significantly by wakefulness level while beta oscillation scaling exponent significantly increased in the closed eye condition. Increased synaptic activity associated with arousal/wakefulness may interfere with dynamics of LRTC. Study confirmed existence of LRTC in both awake and closed eyes but more consistently in closed eye state and may be reflective of underlying SOC.
Weiss et al., 2011	22 healthy adults	EEG during REM, NREM2, NREM4 sleep	Hurst exponent, power spectral measures	• Study assessed various metrics of sleep EEG including monofractal, multifractal, and spectral power measures. Sleep stage discrimination with multifractal measure was superior to relative band powers, spectral edge frequency, or Hurst exponent. • Study found higher H exponent, DFA exponent, and fractal exponent in deep sleep, while multifractal measure was decreased. These findings indicate a decrease of multifractality and an increase in long memory in deep sleep.
Dehghani et al., 2012	2 adult patients with intractable epilepsy	iEEG from temporal gyrus in awake state, REM, and slow-wave sleep	Power-law estimation*	• Study investigated power-law distribution of neuronal avalanches (spikes) from iEEG data. Neuronal avalanches (spikes) did not clearly follow power-law in awake, SWS, or REM states and instead followed closer to exponential distribution. Positive and negative LFPs followed apparent power laws with log-log analysis but closer examination with CDF-based testing did not confirm power law and favored double exponential distribution. In cases where power laws were seen with log-log analysis, exponents were too high for SOC systems. • These results contradict those of prior studies (Petermann et al., 2009; Ribeiro et al., 2010) and perhaps could be harmonized with prior results by taking into account recording methods or volume conduction effects.
Meisel et al., 2013	8 healthy adults	EEG during 40 h of sustained wakefulness	Power-law estimation*, branching parameter, spectral density	• Study evaluated evolution of criticality parameters during prolonged wakefulness. At the start of sleep deprivation, coherence potentials were organized as neuronal avalanches in space and time with power law −3/2 and branching parameter 1.17, both of which suggest a system near criticality. With increased duration of wakefulness, size distributions of coherence potentials and PLIs developed larger tails, an increase in branching parameter, and an increase in mean synchronization while variability of synchronization decreased. • These findings suggested that, during sustained wakefulness, the neural networks move from a critical to a supercritical state, perhaps as a result of increased excitation and decreased inhibition (Shew et al., 2009; Yang et al., 2012). Sleep might serve to reorganize network dynamics to critical state in order to assure optimal computational capabilities while awake.
Priesemann et al., 2013	5 adults with refractory epilepsy	iEEG (depth electrode)	Power-law estimation*, branching parameter	• Neuronal avalanches were recorded from intracranial depth electrodes in 5 epilepsy patients over two nights through all sleep stages. Avalanches were described by power laws in all cases but with different dynamics depending on sleep stages. SWS showed the largest avalanches, wakefulness showed intermediate-sized, while REM showed smallest. Differences in avalanche distributions implied that not all vigilance states could be derived from SOC. • Modeling suggested that human brain operates within subcritical regime, near criticality where differences between vigilance states can be mediated by small changes in effective synaptic strength which allow the brain to tune closer to criticality (SWS) or farther away (REM). SWS showed increased correlations between cortical areas due to increased criticality, while REM sleep showed more fragmented dynamics than SWS and wakefulness.
Lo et al., 2013	48 healthy adults and 48 age-matched adults with obstructive sleep apnea (OSA)	Polysomnogram recorded for 2 consecutive nights	Probability transfer matrix, power-law estimation	• Study found a power law distribution of wake and arousal durations in sleep using log-log analysis. Power-law exponents were different between patients with OSA and healthy controls. • Using novel probability transfer matrix and SOC, authors revealed sleep transition pathways that could be reduced to two basic and independent transition paths. Study also found that sleep micro-architecture at scales from seconds to minutes exhibits a non-equilibrium behavior reminiscent of critical systems.
Tagliazucchi et al., 2013	63 healthy adults	fMRI and EEG during NREM sleep	DFA	• Study hypothesized that breakdown of LRTC would occur during descent into deep sleep. Authors found that Hurst exponent decreased during N2
				sleep confined to DMN and attention networks. Study also discovered that autocorrelation in fronto-parietal areas diminish from wakefulness to deep sleep.
Allegrini et al., 2013	29 healthy adults	Polysomnogram	Random walks, DFA, fractal intermittency	• Study hypothesized that a renewal point process describing fractal intermittency could be a correlate of consciousness. Fractal intermittency can be seen in EEG data by sequence of global rapid transition processes (RTP) with power law distribution of waiting times. During sleep, Hurst exponent switched from 0.75 in wake and REM phases to 0.5 in deep sleep, suggesting fractal intermittency in wake and REM but short-time correlations in SWS.
Allegrini et al., 2015	29 healthy adults	Polysomnogram	Random walks, DFA, fractal intermittency	• Study evaluated fractal intermittency (see Allegrini et al., 2013) during sleep. While critical avalanches remained unchanged, there was a breakdown in intermittency and functional connectivity during shallow and deep NREM sleep. The authors provided a theory for fragmentation-induced intermittency breakdown. The possible role of critical avalanches in dreamless sleep is to provide rapid recovery of consciousness if stimuli arouse the person out of sleep.
Colombo et al., 2016	52 adults with insomnia disorder (ID), 42 age- and sex-matched controls	High-density EEG with eyes-open (EO) and eyes-closed (EC)	DFA	• There were no differences in DFA exponents between ID and controls in any frequency bands during EO or EC. However, during EO, individuals with worse sleep quality had stronger LRTC, suggesting that subjective insomnia complaints involve distinct processes in people with ID and controls. However, the measurement of insomnia severity was based on subjective report, not polysomnography. Future studies should examine polysomnographic data as well as examine frequency (rather than amplitude) fluctuations.
Meisel et al., 2017	8 healthy adults	EEG during 40 h of sustained wakefulness	DFA, autocorrelation function, spectral density	• Study evaluated LRTCs in resting state human EEG during 40-h sleep deprivation experiment. LRTCs declined as sleep deprivation progressed, even when taking into account changes in signal power. LRTCs naturally emerged in vicinity of critical state. Authors argued that the increased LRTCs seen in insomnia patients (Colombo et al., 2016) could be due to signal power changes associated with worse sleep quality.
Bocaccio et al., 2019	18 healthy adults	fMRI and EEG during wakefulness and all sleep stages	Power-law estimation*	• Study observed scale-free hierarchy of co-activated connected clusters using point-process transformation of fMRI data recorded during wake and NREM sleep. Sleep stage had significant impact on scaling parameter of power law, which was robust to spatial coarse-graining, alternative statistical models, and disappearing with phase shuffling of fMRI time series. These findings suggest the existence of larger clusters or avalanches during N2 sleep. Criticality may help with the “pretty hard problem of consciousness” by offering metrics that behave one way in conscious states and differently in another.

Asterisk (*) represents power-law estimations that meet criteria equivalent to or more stringent than Clauset et al. (2009). SWS, slow-wave sleep; REM, rapid eye-movement; NREM, non-rapid eye-movement; PLI, phase-locking interval; DMN, default mode network.